Find the values of the following expressions if $x = 3$ and $y = 5$ - Junior Cycle Mathematics - Question 10 - 2013
Question 10
Find the values of the following expressions if $x = 3$ and $y = 5$.
(i) 5$x + 4$y
(ii) $x^2 + y^2$
(iii) Multiply $5(3a - 4b)$.
(ii) Multiply $x( x - y) + y( x ... show full transcript
Worked Solution & Example Answer:Find the values of the following expressions if $x = 3$ and $y = 5$ - Junior Cycle Mathematics - Question 10 - 2013
Step 1
(i) 5$x + 4$y
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Answer
To find the value of the expression 5x+4y:
Substituting the values of x and y:
5(3)+4(5)=15+20=35
Step 2
(ii) $x^2 + y^2$
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Answer
To evaluate the expression x2+y2:
Substituting the values of x and y:
32+52=9+25=34
Step 3
(i) Multiply $5(3a - 4b)$
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Answer
To multiply the expression:
5(3a−4b)=15a−20b
Step 4
(ii) Multiply $x( x - y) + y( x + y)$
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Answer
To simplify the expression:
Expand x(x−y) and y(x+y):
x2−xy+xy+y2
Combine like terms:
x2+y2
Step 5
(i) $4xy - 6x^2y^2$
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Answer
To factorise:
Factor out the common term 2y:
4xy−6x2y2=2y(2x−3x2)
Step 6
(ii) $2ax - ay + 2bx - by$
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Answer
To factorise:
Group the terms:
ay(2x−y)+b(2x−y)
Factor out (2x−y):
(a+b)(2x−y)
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